Germany's constitutional court has begun hearing a case that will decide whether Angela Merkel's government was right to agree to last year's multimillion-euro bailout of Greece and the accompanying rescue package for other faltering EU countries.

In the unlikely event that the complainants win, the payments will be blocked, an outcome experts say would shake the foundations of the European Union. "If the court were to restrict the government's leeway to act, the consequences for the EU and the financial markets could be extremely serious," said Commerzbank analyst Eckart Tuchtfeld.

Plaintiffs include MP Peter Gauweiler, a renegade member of Chancellor Merkel's conservative bloc. He has a history of challenging European Union initiatives and in 2009 he brought a complaint against the integration measures dictated by the Treaty of Lisbon, with limited success.

Gauweiler, along with a group of professors, argues the measures violate EU no-bailout provisions and German constitutional clauses protecting property and democracy. They have the support of the majority of ordinary Germans, who were fiercely opposed to "their money" being used to bail out less prudent countries.

The case is so crucial that Merkel dispatched her finance minister, Wolfgang Schäuble, to give evidence at Tuesday's hearing in Karlsruhe. Inside the court, he defended the rescue packages for Greece and other eurozone countries, arguing that "the stability of the euro is of paramount significance".

He pointed to the risk of financial instability across Europe and beyond at the time when the government signed on to the initial Greek rescue of May 2010 and also the wider eurozone fund created shortly afterward.

Those plans foresee Germany, Europe's biggest economy, guaranteeing loans up to €22.4bn for Greece and €147.6bn (£20.1bn) for other countries.

The constitutional court's president Andreas Vosskuhle said the court did not want to hear a debate on the measures' economic merits, and that the right economic strategy was a matter for politicians and not judges. But, he said, his court "has to consider the limits that the constitution sets for politicians."

Eurosceptic law professor Karl Albrecht Schachtschneider insisted that "what is economically wrong can't be legally right". He argued that the rescue measures violated a no-bailout provision in the European Union's Lisbon treaty without sufficient justification.

He also contended that they violated German constitutional clauses protecting property and democracy, the latter by restricting the German parliament's control over its own budget.

"A union of liability and debt favouring other states has been created," he said.

Gauweiler's representative, Prof Dietrich Murswiek, pointed to current efforts to set up a second Greek rescue package, arguing that loans would sink into a "bottomless pit".

"It's like trying to repair water damage by blowing up the house," he said.

Murswiek contended: "The rescue fund serves in reality to take risks away from certain big banks," which would be unconstitutional.

Schäuble said the government was on solid legal ground, and argued that "we Germans benefit even more than other Europeans from the currency union".

A ruling is expected this year. Most analysts expect the court to rule the bailouts were legal but to attach strings to the deals. Last month, Vosskuhle, the chief judge hearing the case, seemed to hint at this, when said there were instances in which the European Union could violate the core of Germany's constitutional identity. Such a "sensitive constellation" was indeed conceivable, he said, adding that he believed that this would "not necessarily happen in the near future".

The Greek debt crisis could turn into a European banking crisis, according to some economists. But is there any solution to the conundrum that protects living standards and pacifies the markets? With Martin Kettle, Phillip Inman, Aris Chatzistefanou and Aditya Chakrabortty